Bessel Bessel-Maitland Generalized Bessel-Maitland Wright Generalized Lommel-Wright Functions Cauchy-Hadamard Abel and Tauber Theorems 30B10 30B30 33C10 33C20
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Fractional Calculus and Applied Analysis, Vol. 10, No 1, (2007), 59p-74p
The classical Cauchy-Hadamard, Abel and Tauber theorems provide
useful information on the convergence of the power series in complex plane.
In this paper we prove analogous theorems for series in the generalized
Lommel-Wright functions with 4 indices. Results for interesting special
cases of series involving Bessel, Bessel-Maitland, Lommel and Struve functions,
are derived.We provide also a new asymptotic formula for the generalized
Lommel-Wright functions in the case of large values of the index ν
that are used in the proofs of the Cauchy-Hadamard, Abel and Tauber type
theorems for the considered series.